Some studies of magnetohydrodynamic oscillations of a rotating fluid

Abstract

Some theoretical studies on the propagation of Rossby-MHD waves in homogeneous media and the reflection of Rossby-MHD and inertial-MHD waves at rigid boundaries are presented. The evolution of an initial Rossby-MHD disturbance on a beta-plane is studied by the method of stationary phase in two dimensions. For positive β, long wavelength magnetic modes of this wave travel eastwards and propagate in a triangular region of the beta-plane. To an observer moving with the group velocity of a particular wave, its amplitude appears to diminish with time t as a function of t(^-1).The reflection of a Rossby-MHD wave by a conducting or insulating rigid boundary generates two reflected modes, one of which may be a non-propagating wave. The wavenumbers, group velocities, magnetic/kinetic energy ratios and energy densities of the incident and reflected waves are, in general, different. For waves of planetary dimensions, an eastwards travelling magnetic mode, on reflection from a N-S boundary, is transformed entirely into a long wavelength inertial mode and a large conversion of magnetic energy into kinetic energy is observed. An inertial-MHD wave on reflection from a conducting or an insulating rigid boundary splits up into three reflected modes one of which is always a travelling magnetic mode. The wavenumbers, group velocities, magnetic to kinetic energy ratios and energy densities of the incident and reflected waves are not equal. Although, the reflection of any of these modes always generates a reflected magnetic mode, no travelling inertial modes may be generated for certain orientations of the boundary. In the long term this phenomenon will increase the share of the energy of the magnetic modes at the expense of the inertial modes.